**4.3 Depth distribution of rock strength, brittleness and earthquake activity caused by the fan mechanism**

**Figure 17d** shows a typical histogram of depth distribution of earthquake frequency (from [7]). It demonstrates that earthquake activity varies with depth and has a maximum at a certain depth. Today there are two fundamentally different explanations for this earthquake feature. Both of them consider earthquakes as stick-slip instability on pre-existing faults. The first one is based on the fact that the frictional strength (determining the lithospheric strength) in the upper crust increases with depth in accordance with Byerlee's friction law [10], while in the lower crust it decreases accordingly to a high-temperature steady-state flow law [2, 7]. The second one is based on the velocity-weakening and velocity-strengthening concept [7, 9]. We introduce here a new concept which is based on the new understanding about (unknown before) properties of hard rocks at seismic depth's caused by the fan mechanism [20, 23, 42].

**Figure 17a**–**c** shows symbolically depth distribution of the fan-mechanism efficiency, rock strength profiles and rock brittleness. These graphs are analogous to the dependencies discussed in **Figures 11** and **12**. The fan mechanism can operate at depths where temperature (rising with depths) does not prevent the fan-hinged shear. The new strength profile for hard rocks in **Figure 17b** shows that at low depths corresponding to σ3 < σ3fan(min), the lithospheric strength is determined solely by frictional strength τf. At greater depths corresponding to the range of the fan-mechanism activity, the situation is specific. In the absence of conditions for

#### **Figure 17.**

*Relation between depth distribution of the fan-mechanism efficiency, rock strength, rock brittleness and earthquake frequency.*

*Earth Crust*

fragment is located at great depth where the minor stress σ3 is high enough for the fan-mechanism activation in intact rock. Horizontal lines on the graph below indicate symbolically levels of the following parameters: τs is the strength of intact rock, τf is the frictional strength of pre-existing fault, τfan is the transient strength of intact rock determined by the fan mechanism, τ0 is the field shear stress applied to the rock fragment, τ1 is the field stress after the rupture propagation and ∆τ is the

stress drop. Orientation of the field shear stress is shown by open arrows.

at the stick-slip process in the case of activation of the pre-existing fault.

Thus, the fan mechanism favours the generation of new faults in hard intact rock mass adjoining a pre-existing fault in preference to frictional stick-slip instability along the pre-existing fault. Each earthquake generated by the fan mechanism is associated with formation of a new fault at a new location in the vicinity of a preexisting fault. Furthermore, each new fault can serve as a stress concentrator for generation of the next new fault. The proximity of the pre-existing fault to the zone of dynamic new fracture development in intact rock creates the illusion of frictional stick-slip instability of the pre-existing fault, thus concealing the real situation.

At the same time, there are many evidences that earthquakes are associated with the formation of new faults in the proximity of pre-existing faults. For example, **Figure 16** shows maps of earthquakes in a New Zealand region of relative motions between the Australian and Pacific plates which are not accommodated on one general fault, but on many faults across a wide zone. **Figure 16a** (from [40]) shows

*Maps of spatial distribution of earthquake hypocentres and faults on the earth's surface for a New Zealand* 

Because the level of field stress τ0 is significantly less than the frictional strength τf, the situation on the pre-existing fault is very stable. However, due to deformations along the fault caused by shear stresses τ0, a high local stress can be created in the jog zone delineated by a red circle. If the local stress in intact rock of this zone reaches the level of rupture strength τs, the fan structure can be formed. After formation of the fan structure, it can propagate spontaneously through intact rock mass at low shear stresses τ<sup>0</sup> in accordance with Class III behaviour discussed in **Figure 3** and generate an earthquake. The new fault is shown by a white line, and the propagating fan head is represented by red ellipsis. Due to very high brittleness of this rock associated with extremely low rupture energy provided by the fan mechanism, the failure process can be accompanied by abnormal energy release and violence. It should be emphasised that despite the fact that the new fault is formed in intact rock, the magnitude of stress drop ∆τ can be very low because this process takes place at low shear stress applied. The stress drop can be even less than

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**Figure 16.**

*region [40, 41].*

#### **Figure 18.**

*Illustration of depth distribution for rock transient strength, brittleness and earthquake frequency in the Earth's crust represented by two layers of rocks of different hardness.*

activation of the fan mechanism, the lithospheric strength is determined by friction. However, if the fan mechanism is activated somewhere causing the new rupture development in intact rock, the transient lithospheric strength in that region decreases to the level τfan. After completion of the failure process, the lithospheric strength returns to the frictional strength.

It should be noted that the improved concept of the lithospheric strength incorporates all three types of rock strength determining the instability in the seismic layer: fracture strength τs, frictional strength τf and fan strength τfan. The fracture strength determines the level of local stress at which the initial fan structure can be generated. The shaded area between the frictional τf and the fan-transient τfan profiles determines levels of field stress under which an initiated fan structure can propagate creating an earthquake. Importantly, the fan mechanism can cause earthquakes at any level of field stress τ within the shaded zone. Due to this the highest probability of events is at a depth characterised by the maximum range between τfan and τf. This depth corresponds approximately to the depth of optimal efficiency of the fan mechanism, where the rock mass is characterised by the minimum transient strength and maximum brittleness. At lower and greater depths, the probability decreases. This feature determines the typical depth-frequency distribution of earthquake hypocentres. The upper and lower cut-offs represent boundaries of the zone of the fan-mechanism activity. The explanation for the depth distribution of earthquake frequency on the basis of the fan mechanism differs fundamentally from the conventional explanations.

On the basis of the fan mechanism, it is possible also to explain the existence of a few zones of earthquake activity with depth. As discussed in **Figure 12**, the efficiency of the fan mechanism depends on the rock hardness (UCS): the harder the rock, the greater the fan-mechanism efficiency and the wider the confining pressure range over which the fan mechanism is active. **Figure 18a** illustrates schematically depth distributions of the fan-mechanism activity for four rocks characterised by different hardness, with strength increasing from rock 1 to rock 4. **Figure 18b** shows a situation when the earth's crust is represented by two layers of rocks of different hardness (rock 1 and rock 3). In this case, two zones of earthquake activity may be observed. Rock 1 will exhibit the typical (complete) form of earthquake

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**Author details**

Boris Tarasov

provided the original work is properly cited.

The Far Eastern Federal University, Vladivostok, Russia

\*Address all correspondence to: bgtaras@gmail.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic…*

frequency-depth distribution, while rock 3 will show a truncated form. Such features of earthquake behaviour have been observed in nature and explained on the basis of

The fan theory proposes new explanations for a number of other abnormalities and paradoxes associated with extreme rupture dynamics (including supershears) observed in natural and laboratory conditions [19, 20, 43]. Mathematical models were developed which allow studying unique features of the fan mechanism and simulating the process of extreme rupture development at different loading conditions [43–46].

This work was supported by the Ministry of Science and Education of the

conventional velocity-weakening and velocity-strengthening approach [9].

*DOI: http://dx.doi.org/10.5772/intechopen.85413*

Russian Federation (grant no. RFMEFI58418X0034).

**Acknowledgements**

*Dramatic Weakening and Embrittlement of Intact Hard Rocks in the Earth's Crust at Seismic… DOI: http://dx.doi.org/10.5772/intechopen.85413*

frequency-depth distribution, while rock 3 will show a truncated form. Such features of earthquake behaviour have been observed in nature and explained on the basis of conventional velocity-weakening and velocity-strengthening approach [9].

The fan theory proposes new explanations for a number of other abnormalities and paradoxes associated with extreme rupture dynamics (including supershears) observed in natural and laboratory conditions [19, 20, 43]. Mathematical models were developed which allow studying unique features of the fan mechanism and simulating the process of extreme rupture development at different loading conditions [43–46].
